I understand how a linearization of a multivariable function creates a tangent plane that can be used to estimate points on the actual function and it will either overestimate or underestimate the true value of the function. However, I don't understand what properties of the function allows this to consistently happen. I know in the 2d plane concavity of the function determines this with the second derivative test, can a similar idea be used here?
2026-04-02 18:11:19.1775153479
What properties of a multivariable function f(x,y) makes a linearization over or underestimate the true value of a point?
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